Upload Progress with PHP 7.1 and NGINX

While working on a Drupal 8 project served by NGINX and PHP-FPM, the status report looked great aside from UPLOAD PROGRESS at the bottom:

Your server is capable of displaying file upload progress, but does not have the required libraries. It is recommended to install the PECL uploadprogress library.

As of Drupal 8.3.5, Drupal will complain until you install that PECL library, even if you’re using the NGINX Upload Progress module. The current php-uploadprogress package from Ondřej Surý’s excellent PPA doesn’t currently install uploadprogress.ini into /etc/php/7.1/mods_available/, but it can be used anyway or the module can be compiled from source.